Find a1 and d for an arithmetic sequence with these terms. a3=-8 and a7=32


We know that the formula for the arithmetic sequence is an = a1 + (n - 1)*d where a1  is the first term n is the numbers of terms for n=3   a3=-8 -8=a1+(3-1)*d-----> -8=a1+2*d-----> equation 1 for n=7   a7=32 -32=a1+(7-1)*d----> -32=a1+6*d----> equation 2 multiply equation 2 by -1-----> 32=-a1-6*d------> equation 3 add equation 1 and equation 3 -8=a1+2*d 32=-a1-6*d ---------------- 24=-4*d------> d=-6 -8=a1+2*(-6)    (substitute the value of d in equation 1) -8=a1-12-----> a1=-8+12-----> a1=4 the answer is a1=4 d=-6

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